Does the Curl Relationship Exist in Both Directions for Vector Fields?

AI Thread Summary
The discussion centers on the relationship between vector fields and their curls in electrodynamics, specifically regarding magnetic potential. The initial claim suggested that if B is the curl of A, then A could also be expressed as the curl of B. However, it was clarified that this is incorrect, and the relationship does not exist in both directions. The final consensus is that the curl relationship is not reversible. This conclusion emphasizes the importance of understanding the properties of vector fields in electrodynamics.
hisotaso
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hisotaso said:
We are studying electrodynamics, more specifically magnetic potential. We are given

B=∇xA

I saw on a certain website here http://www.ittc.ku.edu/~jstiles/220/handouts/The Magnetic Vector Potential.pdf that

A=∇xB

So is it true in general that for a vector field, the curl relationship exists in both directions as shown above?


Where does it say A=∇xB?

This is wrong.
 
Looks like I read it wrong. My mistake. Back to my question: the answer is no?
 
Yep. The answer in no.
 
Thank you.
 

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